document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=407470>Question 407470</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write an equation that satifies set of conditions listed below.\r<BR>\n" );
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document.write( "A hyperbola with foci (0,-sqrt(6))and (0,sqrt(6))and asymptotes y=(sqrt(2)/2) and y=(-sqrt(2)/2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #287499 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=287499\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Write an equation that satifies set of conditions listed below.A hyperbola with foci (0,-sqrt(6))and (0,sqrt(6))and asymptotes y=(sqrt(2)/2) and y=(-sqrt(2)/2)<BR>\n" );
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document.write( "y=(-sqrt(2)/2)=-1.414x/2<BR>\n" );
document.write( "y=(sqrt(2)/2)=1.414x/2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "given hyperbola has a vertical transverse axis,x=0. (hyperbola opens up and down)<BR>\n" );
document.write( "Center is on this line between foci=(0,0)<BR>\n" );
document.write( "Asymptotes=+-a/b=sqrt(2)/2<BR>\n" );
document.write( "so,a=sqrt(2)<BR>\n" );
document.write( "a^2=2<BR>\n" );
document.write( "b=2<BR>\n" );
document.write( "b^2=4<BR>\n" );
document.write( "a and b also represent the legs of a right triangle in which c, the focal point is the hpotenuse.  <BR>\n" );
document.write( "c^2=a^2+b^2<BR>\n" );
document.write( "c=sqrt(2+4)=sqrt(6)<BR>\n" );
document.write( "Equation of the hyperbola:<BR>\n" );
document.write( "y^2/2+x^2/4=1<BR>\n" );
document.write( "The graph will look much like the graph below:<BR>\n" );
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document.write( "y=(((x^2)+4)/2)^.5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-4%2C+4%2C+-4%2C+4%2C%28%28%28x%5E2%29%2B4%29%2F2%29%5E.5%2C-%28%28%28x%5E2%29%2B4%29%2F2%29%5E.5%0D%0A%2C1.414x%2F2%2C-1.414x%2F2%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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